# Darcy-Weisbach Equation

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Darcy-Weisbach Equation, abbreviated as DW, a dimensionless number, is the most common way of expressing the pressure drop of a piped fluid.  The equation is valid for fully developed, steady state and incompressible flow. The Darcy-Weisbach equation with the Moody Diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow.

### Darcy-Weisbach Equation FORMULA

(Eq. 1)  $$\large{ h_l = \frac { f_d \; l \; v^2 } { 2 \; d \; g } }$$

(Eq. 2)  $$\large{ h_l = f_d \; \frac{ l }{ d } \; \frac{ v^2}{ 2 \; g} }$$

Where:

$$\large{ h_l }$$ = head loss

$$\large{ v }$$ = mean flow velocity

$$\large{ f_d }$$ = Darcy friction factor

$$\large{ g }$$ = gravitational acceleration

$$\large{ d }$$ = pipe inside diameter (ID)

$$\large{ l }$$ = pipe length

Solve for:

$$\large{ v = \sqrt { \frac { 2 \; h_l \; d \; g } { f_d \; l } } }$$

$$\large{ f_d = \frac { 2 \; h_l \; d \; g } { l \; v^2 } }$$

$$\large{ g = \frac { f_d \; l \; v^2 } { 2 \; h_l \; d } }$$

$$\large{ d = \frac { f_d \; l \; v^2 } { 2 \; h_l \; g } }$$

$$\large{ l = \frac { 2 \; h_l \; d \; g } { f_d \; v^2 } }$$